SOLUTION: if the parabola y-2=a(x-3)exponent 2 goes through the point (2,0), what is the value of a ?

Question 49111: if the parabola y-2=a(x-3)exponent 2 goes through the point (2,0), what is the value of a ?
Answer by Born2TeachMath(20) (Show Source): You can put this solution on YOUR website!
Given the parabola y-2 = a(x-3)^2 goes through the point (2, 0), this means that algebraically, if you plug in x = 2 and y = 0, then the equation will be true (the left side will equal the right side). Therefore, to find the value of "a", plug in x = 2 and y = 0 and then just solve for "a"
y-2 = a(x-3)^2
0-2 = a(2-3)^2
-2 = a(-1)^2
-2 = a(1) since (-1)^2 = 1
-2 = a since a(1) = a
So the value of a needed to make the parabola y-2 = a(x-3)^2 pass through the point (2, 0) is a = -2
Remember - the key here is to know that if a given point "lies on a graph", the the values of the point plugged into the equaiont for the graph makes the left side equal to the right side when both are evaluated!
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